Atkin-Lehner |
3- 5+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
84825n |
Isogeny class |
Conductor |
84825 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
15566712890625 = 36 · 59 · 13 · 292 |
Discriminant |
Eigenvalues |
1 3- 5+ 0 -6 13+ 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-9792,323491] |
[a1,a2,a3,a4,a6] |
Generators |
[-858:3329:8] [-42:833:1] |
Generators of the group modulo torsion |
j |
9116230969/1366625 |
j-invariant |
L |
12.520493421328 |
L(r)(E,1)/r! |
Ω |
0.66978114602601 |
Real period |
R |
9.3467048865766 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000265 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9425c1 16965r1 |
Quadratic twists by: -3 5 |